Idea: vovuh

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
for (int pw = 2; pw < 30; ++pw) {
int val = (1 << pw) - 1;
if (n % val == 0) {
cerr << val << endl;
cout << n / val << endl;
break;
}
}
}
return 0;
}
```

Idea: vovuh

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
n /= 2;
if (n & 1) {
cout << "NO" << endl;
continue;
}
cout << "YES" << endl;
for (int i = 1; i <= n; ++i) {
cout << i * 2 << " ";
}
for (int i = 1; i < n; ++i) {
cout << i * 2 - 1 << " ";
}
cout << 3 * n - 1 << endl;
}
return 0;
}
```

1343C - Alternating Subsequence

Idea: vovuh and MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
auto sgn = [&](int x) {
if (x > 0) return 1;
else return -1;
};
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
vector<int> a(n);
for (auto &it : a) cin >> it;
long long sum = 0;
for (int i = 0; i < n; ++i) {
int cur = a[i];
int j = i;
while (j < n && sgn(a[i]) == sgn(a[j])) {
cur = max(cur, a[j]);
++j;
}
sum += cur;
i = j - 1;
}
cout << sum << endl;
}
return 0;
}
```

1343D - Constant Palindrome Sum

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int t;
cin >> t;
while (t--) {
int n, k;
cin >> n >> k;
vector<int> a(n);
for (auto &it : a) cin >> it;
vector<int> cnt(2 * k + 1);
for (int i = 0; i < n / 2; ++i) {
++cnt[a[i] + a[n - i - 1]];
}
vector<int> pref(2 * k + 2);
for (int i = 0; i < n / 2; ++i) {
int l1 = 1 + a[i], r1 = k + a[i];
int l2 = 1 + a[n - i - 1], r2 = k + a[n - i - 1];
assert(max(l1, l2) <= min(r1, r2));
++pref[min(l1, l2)];
--pref[max(r1, r2) + 1];
}
for (int i = 1; i <= 2 * k + 1; ++i) {
pref[i] += pref[i - 1];
}
int ans = 1e9;
for (int sum = 2; sum <= 2 * k; ++sum) {
ans = min(ans, (pref[sum] - cnt[sum]) + (n / 2 - pref[sum]) * 2);
}
cout << ans << endl;
}
return 0;
}
```

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
vector<vector<int>> g;
void bfs(int s, vector<int> &d) {
d[s] = 0;
queue<int> q;
q.push(s);
while (!q.empty()) {
int v = q.front();
q.pop();
for (auto to : g[v]) {
if (d[to] == INF) {
d[to] = d[v] + 1;
q.push(to);
}
}
}
}
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int t;
cin >> t;
while (t--) {
int n, m, a, b, c;
cin >> n >> m >> a >> b >> c;
--a, --b, --c;
vector<int> p(m);
for (auto &it : p) cin >> it;
sort(p.begin(), p.end());
vector<long long> pref(m + 1);
for (int i = 0; i < m; ++i) {
pref[i + 1] = pref[i] + p[i];
}
g = vector<vector<int>>(n);
for (int i = 0; i < m; ++i) {
int x, y;
cin >> x >> y;
--x, --y;
g[x].push_back(y);
g[y].push_back(x);
}
vector<int> da(n, INF), db(n, INF), dc(n, INF);
bfs(a, da);
bfs(b, db);
bfs(c, dc);
long long ans = 1e18;
for (int i = 0; i < n; ++i) {
if (da[i] + db[i] + dc[i] > m) continue;
ans = min(ans, pref[db[i]] + pref[da[i] + db[i] + dc[i]]);
}
cout << ans << endl;
}
return 0;
}
```

1343F - Restore the Permutation by Sorted Segments

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
vector<set<int>> segs;
for (int i = 0; i < n - 1; ++i) {
set<int> cur;
int k;
cin >> k;
for (int j = 0; j < k; ++j) {
int x;
cin >> x;
cur.insert(x);
}
segs.push_back(cur);
}
for (int fst = 1; fst <= n; ++fst) {
vector<int> ans;
bool ok = true;
vector<set<int>> cur = segs;
for (auto &it : cur) if (it.count(fst)) it.erase(fst);
ans.push_back(fst);
for (int i = 1; i < n; ++i) {
int cnt1 = 0;
int nxt = -1;
for (auto &it : cur) if (it.size() == 1) {
++cnt1;
nxt = *it.begin();
}
if (cnt1 != 1) {
ok = false;
break;
}
for (auto &it : cur) if (it.count(nxt)) it.erase(nxt);
ans.push_back(nxt);
}
if (ok) {
set<set<int>> all(segs.begin(), segs.end());
for (int i = 1; i < n; ++i) {
set<int> seg;
seg.insert(ans[i]);
bool found = false;
for (int j = i - 1; j >= 0; --j) {
seg.insert(ans[j]);
if (all.count(seg)) {
found = true;
all.erase(seg);
break;
}
}
if (!found) ok = false;
}
}
if (ok) {
for (auto it : ans) cout << it << " ";
cout << endl;
break;
}
}
}
return 0;
}
```

How Problem D can be solved using scanline algo?

Well, I can explain it rough. The thing is that there are $$$O(n)$$$ (actually at most $$$2n$$$) endpoints of these segments (the second case) and $$$O(n)$$$ (at most $$$n$$$) sums of kind $$$a_i + a_{n-i+1}$$$ (the first case). And the idea is that you are only interested in these $$$3n$$$ points (maybe with some adjacent points also). This is because in other points values of $$$pref$$$ and $$$cnt$$$ don't change at all. So you can compress coordinates and then just consider all segments as events going from left to right and changing the value of $$$pref$$$ correspondingly and store $$$cnt$$$ in some logarithmic data structure like map in C++.

I have implemented an O(nlogn) solution using compression here. For those of you who are confused, check it out!

what exactly is pref adding up

pref[x] stores the number of pairs whose sum can be made equal to x with less than 2 operations (the same as editorial pref).

I guess i over-killed the over-kill...

greetings! @vovuh can you suggest me any tutorial,book,pdf,blog etc from where i can learn some fundamental techniques like prefix sum or anything that are frequently needed in codeforces contest problems.Thanks in advance your editorials are very clear and easy to understand .thats why i choose those problems where your editorial exists.

you could always search for the cp3 (competitive programming 3) book pdf

@vovuh any link for scanline algo? I can only find it for computer graphics. Is that the one?

I dont't know any good explanations of this "algorithm" because it's more likely approach than algorithm, but I found one tutorial about it, seems good enough.

video editorial of D. Click here

please can anyone check which testcase is failing in my code?77692830

Because I think compared to the tutorials solution it is much simpler code here a link to a submission 77584565

Can you please explain your solution? Thanks

Vovuh did above. Every pair of values in our array can be splitted into 5 parts.

Let be min the min of the two values in the array, and max the bigger.

First part where x is so low that we must decrease both numbers, so if x is in this interval the pair contributes +2

if $$$x>=min+1$$$ the pair contributes +1

if $$$x==min+max$$$ the pair contributes 0

if $$$x<=max+k$$$ the pair contributes +1

if $$$x>max+k$$$ the pair contributes +2

Then we create an array of size maximal possible x, and insert the above numbers. Then the prefix sum at position i of the array is the number of operations we need if x==i. So we choose the smallest of them as answer.

Note that this runs in O(n), and if k would have had huge constraints, we would simply use a map instead of an array for evt.

Yeah man, I used the same approach.

https://ideone.com/1gdDsO

Yeah,

highfiveWhat do you mean by events. Are these points or segments?

The word "event" comes from typical problems which are solved with this algo.

In the simple version of the problem we want to find how much of a set of given intervals overlap at some point, or where is the point with most/less overlaps.

Then there are two kind of events while we loop though the intervals, this is start of an interval, and end of an interval. At start we do +1, at end we do -1.

We loop throug the sorted list of events. The body of the loop kind of looks like an event handler.

Example tutorial

Hey is scanline and prefix sum trick the same thing?? Looking at your solution I see it as a mix of coordinate comp and prefix sum trick.. Pls Correct me if I'm wrong.

Scanline and prefix sums are two different things. However, both are used in this problem.

Sire, please have a look at my BRUTE FORCE solution for D and tell me what's wrong in it. I'd be grateful:

Let's say you call for function numberOfChanges(v, i) for i =2*k and in function: in vector v , if a pair {1,1} exists then you are incrementing sum by 1 , but it has to increased by 2. Hope you got it, check you conditions for incrementing sum in function numberOfChanges(v, i) , otherwise it looks fine.

Won't it increment by one as the changed pair can be {1, 2*k-1}?

Sorry, tried deleting this but couldn't

ok no harm done.xD

value of an element can be in range [1:k].

Thanks for the tutorial <3

For Question D is the overall complexity O(k(n+k))? Since the procedure needs to be repeated for each possible x

Why? I'm precalculate three (actually two) parts on $$$O(n+k)$$$ time and then iterate over all possible sums in $$$O(k)$$$ with getting precalculated values in $$$O(1)$$$ time.

ohh I don't think I understand the editorial properly. Why are we calculating prefix sums?

Because you had to know for each point (sum) the number of segments (pairs) covering it. And this is the standard problem that can be solved with prefix sums.

Problem D is really cool, learnt a new thing today. Thanks for the round vovuh

You can check my code (not much pre-computations required)

https://ideone.com/1gdDsO

We first precompute the needed pref[] and cnt[] in O(n+k) so when we repeat the procedure for each possible x we can use the precomputed elements in O(1) making overrall complexity O(n+k)

UPD: Just noticed the question has been answered by vovuh

Can anyone tell me what am I doing wrong in problem E? Here's my submission 77588849

In the graph, I am calculating the minimum distance from a to b, and then b to c. During this, I am storing the frequency of the edges I will visit, and then later assigning the least price to the edge with the highest frequency.

your code will WA answer for the test case 1 5 5 3 1 5 10 5 6 100 80 3 2 1 2 1 4 5 4 5 3 answer is 32 your code is giving 101 means that here you will go from a to b then from b to c via a that will give minimum answer

Here a test case that resembles the graph of 2nd example in the problem.

1 7 9 1 5 7 3 3 5 10000 10000 10000 10000 10000 10000 1 2 1 3 1 4 3 2 3 5 4 2 5 6 1 7 6 7

The optimal output should be 1->7->6->*5*->6->7 then you assign these prices 5,3,3 to get the answer as 5 + 2*(6) = 17.

You cannot do the question on basis of only considering shortest from A to B and then shortest from B to C separately. Consider smallest path from A to B(length s)and there is another path from A to B(length s+1)which has only one more edge then the smallest one.Suppose that path contains C, so that is more advantageous and we need only smallest s+1 prices while with the shortest path we will need then s+k prices (k distance of B from C).

Thank you everyone for helping me figure out my mistake. I really Appreciate it

Can someone explain me solution to problem E in simpler words.

Anyone why my code didn't got accepted..??

https://mirror.codeforces.com/contest/1343/submission/77549512

I guess,it is because of the data type the value overflows so try using long long.

For E why would the optimal path only have 1 or less intersection?

Finally solved one question after joining here few months back in rated. Yaay. Small step forward.

keep it up bro

same here bud, keep going

same here keep it up

In problem F, why would the permutation be unique?

Since the segments have endpoints at $$$2$$$, $$$3$$$, ..., $$$n$$$, at each iterative step you are actually picking the segment that is with endpoint $$$1$$$ greater than the segment you previously picked. There is exactly $$$1$$$ valid segment in each step, which means the reconstruction is unique if an valid permutation exists for you fix of first element.

thanks!

Why is the blog of the solution called Editorial in this blog but called Tutorial here in the contest?

Finally, someone's asking the real questions :P

Thanks for the tutorial. But I don't understand the tutorial of problem E, can anybody help me please?(Please explain me in simpler words) Thank u very much!

here we follow the path: a->x->b->x->c

for every vertex x <= n, find the shortest distances from a to x, b to x, and c to x

since b->x is common, we should distribute minimum weights along this path. Let prefix(i) be sum of i smallest weights.

So the answer will simply be prefix(distance(a to x) + distance(b to x) + distance(c to x)) + prefix(distance(b to x))

Thank you very much, I understand it now.

Can anybody explain problem F I am not able to understand the tutorial

don't go for F now just focus on A,B,C of div2 and A,B,C,D of div3... i am saying this because of my experience in compi beleive me or not i am saying this for your good... keep it up mate....

Why do we need to convert to binary representation, while we can just add 2^0 to (2^0 + 2^1 + ... + 2^(k-1)) = 2^k :D

In Problem D, Can anyone explain why (n/2) — prefix(x) is needed for calculating part 3 of the solution?

See for any particular sum(say x), prefix[x] is having number of pairs that need at most 1 element to be changed. Since for any pair we can make any sum(ofc less than 2k) by changing both the elements so if we have n/2 pairs in total and prefix[x] is number of pair that need at most 1 change so n/2 — prefix[x] is number of pairs which needs both the elements to be changed.

That's because the ones we calculated prefix for are the ones who can reach that x by replacing one element. Thus by subtracting prefix(x) from n/2 and multiplying it by 2 gives us those pairs where we have to change both elements.

Have a look at my submission. I have added comments.

https://mirror.codeforces.com/contest/1343/submission/77603570

Part 3 includes those pairs in which we have to change both values to get the desired sum. Since prefix(x) contains the count of pairs in which we have to change one or none value, hence (n/2)-prefix(x) gives the third part.

In problem E, my approach is —

Find the set of nodes that lie on the shortest path from a to b, stored in

`res1`

.Find the set of nodes from lie on the shortest path c to b, stored in

`res2`

.Find the common nodes (if any) that lie from b, let this be

`equal`

edgesFind the distinct edges, let this be

`diff`

edges = res1.size() + res2.size() — 2 * equal.Then I assign the min values to common edges and the next min values to other

`diff`

nodes.I am getting WA on Test-4. Can anyone tell me where I am doing wrong ?

I get —

`wrong answer 320th numbers differ - expected: '4', found: '6'`

. How to see the 320th tc ?I did the same mistake and got the same WA on the same test case :D. The problem is that you are assuming that the shortest path from a->b->c will comprise of shortest path a->b and shortest path b->c, which is not true..

Why it is not true?

Well I haven't worked it out mathematically, but if you think intuitively, you have to maximize the number of repeating edges while also minimizing the total distance traveled. So it is possible to construct a graph in which a longer path gives you more number of repeated edges, which reduces the total cost, as compared to the shortest path consisting of all distinct edges.

Hey, this is one such case in which this method produces wrong answer — This has been pointed out by someone in the comments above —

The optimal answer to this will be

`32`

.In the D problem. How did we get the value (n/2)-prefx and the final equation also?

Since each element of the array lies between 1 and k, the range of values [min(a[i],a[n-i+1])+1,max(a[i],a[n-i+1])+k] will include the pairs for which the sum equals x as well. Hence pref(x) represents the pairs for which AT MOST 1 needs to be changed. n/2 is the total. Subtract pref(x) from it, we will get the ones which require both elements to be changed. Final equation we need number of changes = (at most 1 change required — no changes required) + 2*(number of pairs which require both elements to be changed)

Last term multiplied by 2 because 2 elements are changed.

Yeah Thanks I got it

Can someone tell how can the solution is found out because i am not getting ++pref[] part code and further code so can anyone explain how the results are generalized..? Problem D

It is on of the popular techniques, it can update in O(1) time and changes are accumulated at the end by calculating the prefix sum.

The range is updated using the index bounds. Consider you want to update the range [l,r] then that can be done adding the +1 to the left bound and -1 at the right corner. So whenever you would be calculating the final results, the following thing happens -:

The +1 is propagated in the range [l, r] since you are adding the previous element to the present element.

The -1 handles the stopping case at r + 1 and now the +1 is neutralized by -1.

Once this array pref is generated, you are now with

sum values which would require just a single modification to reach sum.Since the answer for this overall problem will be :

For the 2nd one, cnt[i] (already having the sum of i beforehand) — pref[i] (which need one element modificationto reach sum i)

For 1st one, the remaining pairs will be the one with 2 modifications, (n / 2) (Total pairs) — pref[i] (sum with one modification to reach i).

Multiplying it by 2 since two modifications are required.

Now try to calculate minimum by iterating over all the possible values of sum [2, 2k].

Sorry for the bad representation. I hope it helps.

hey can anyone tell me why are we doing --pref[max(r1, r2) + 1] in problem D? also why are we calculating prefix sums?

for any pair a[i] and a[n-i-1] we can make it equal to some sum x by changing at most one element a[i] or a[n-i-1] if sum x is in range min(l1,l2) to max(r1,r2). but as sum goes to max(r1,r2)+1 we need to change two elements

we are calculating prefix sum because above argument follows for all sum values that are in range min(l1,l2) to max(r1,r2)

Video editorial of D. Click here

Here is a solution with Explanation for D (Check Here)In case anyone is interested

i got the idea of d and u i.e ranges starting and ending before and after x but can u please explain how did u conclude get =min(d,u)

if u is starting points whom are before x and d is ending points after x then the number of lines where x lies is min(u,d) for example say the ranges are (1,5) , (3,12) (4,8) suppose x = 7 the u=3 and d = 2

So x lies in two ranges which correct i.e. (3,12) and (4,8)

I don't think it's true. As a proof, I've executed your program here.

The core logic of calculating the number of segments intersecting a point is wrong. But somehow your code is AC. So, if I'm missing something here please let me know. I'd be happy to learn.

PS: sorry for necroposting.

Solution of D using Difference Array https://mirror.codeforces.com/contest/1343/submission/77550669

In Problem E, can anyone tell me what should I do if a point is visited again? how would I know if I have assigned an edge some weight more than once? Thanks in advance.

You can ignore overestimates, because it can be shown that vertices that cause overestimates are never the optimal choice for intersection.

A very rough "proof": if the editorial's algorithm assigns more than one cost to a set of edges and thus overestimates the cost, it means that at least two paths among $$$x \rightarrow a, x \rightarrow b,$$$ and $$$x \rightarrow c$$$ overlap. The overlapped edges would form a path from $$$x$$$ to some other vertex $$$y$$$. In this case, $$$y$$$ is always a better choice of intersection.

Thank you. Got it.

why my submission is not showing and also final standing not showing I have solved first 4 qus

It is in queue, wait for the system testing to get over.

How can we use binary search in problem D?? It has tag of binary search. I found out that for making sum of pair from 2 ..... 2*k does not yield a function that has one global optimum...so how we can use binary search on it??

Here is one of some possible arrangement :

n=10k=5array=1 4 2 3 5 2 3 1 4 2sum = changes required

2 = 8

3 = 5

4 = 6

5 = 5

6 = 4

7 = 4

8 = 6

9 = 8

10 = 9

I built a vector that holds the minimum value every pair can take with one change, and a vector that holds the maximum value every pair can take with one change. Fix a target 1 <= x <= 2k that you want every pair to equal after your changes. The number of pairs whose min is > x will require 2 changes, as will the number of pairs whose max is < x. You can binary search for the number of pairs that fulfill these conditions, using something like lower_bound(mins.begin(), mins.end(), x). You'll can also see that a pair cannot fulfill both of these conditions simultaneously, so we don't double count.

Yeh thanks.. now i see we use binary search as our intermediate step and not a primary one. Thank you for explanation!

New to codeforces here, can anyone tell me yesterday I solved 3 problems here but now RED is showing on B and C (even though code is same as editorials) WHY?

It's in queue. Wait for a while

Because currently the system test are running, just wait some half an hour.

Can anyone suggest more problems like D? The prefix sum approach seemed very cool

In problem E why are we checking dist(a,x)+dist(b,x)+dist(c,x)≤m ?

we have our prefix sum array of size M it is practically impossible to have more than M distinct edges weights so This condition is applied to control indexing error If You don't apply it will give you an out of index error for some cases :)

I missed it. Thanks!

your most welcome :)

If someone knows how to solve Problem D using Scanline Please mention your code or any good resources to learn it will be appreciated :)

Div2 D Constant Palindrome Sum Solution using ordered set

Can anyone please explain the segment tree or BIT based approach in problem D that would be helpful??

You can check this soln by Ashishgup https://mirror.codeforces.com/contest/1343/submission/77496545

There is no need to use BIT there, just simple prefix sums would do. It's the same thing, except you're using BIT to develop the prefix sums instead of just doing it directly.

Yeah! BIT is infact developing the same prefix sum , What other approach with BIT is used to solve the problem A/c to you. I am also intrested in the same! :)

I have no clue what other BIT soln people are referring to tbh

can someone explain what problem c actually meant?? still didnt get the problem clearly. thank u.

The given array will consist of some positive and some negative elements. An alternating subsequence will consist of alternating elements (pos,neg,pos,neg... or neg,pos,neg,pos.... and so on). you need to take the max length of alternating sebsequence and find its sum. Remember there could be multiple such subsequence of max size but you need to print the max sum among all.

for D, we can also just check for only those sums that the pairs already make instead of checking all values from 2 to 2*k.In worst case,the maximum value will be n/2, when one element from all the pairs have to be changed.

In the example {6 1 1 7 6 3 4 6}, K = 7. the sum values are 12, 5, 4, and 13. But you get minimum when u make x as 7 or 8 or 9 or 10. So the logic of only checking for sum fails.

In worst case(for example this one),the answer can be at most n/2.I have initialised answer with n/2.whenever x comes out to be anything other than the sums,the answer has to be n/2.

Yeah that is correct, n/2 is the max changes you need to make, but then checking for sum pairs will not suffice.

typedef long long int ll;

## include

## include <bits/stdc++.h>

## include

## include <math.h>

## include <string.h>

using namespace std; int main() { int t; cin >> t; while(t--) { ll n; cin >> n; ll arr[n]; ll brr[n]; for (ll i = 0; i < n;i++) { cin >> arr[i]; if(arr[i]>0) brr[i] = 1; else brr[i] = -1; } ll sum = 0; for (ll i = 0; i < n;i++) { ll lar = arr[i]; ll j = i; int val; if((brr[i]*brr[j])==brr[j]) val = 1; else val = 0; while(j<n && val==1) { lar = max(lar, arr[j]); j++; } sum = sum + lar; i = j — 1; } cout << sum << "\n"; } }

Whats wrong in my code ITS FOR QUESTION C

do you like want downvotes or something? Please format your code

Can anyone please explain how to do problem D with binary search, i tried but couldn't find a way to do it

Can anyone please explain D to me in simple terms? Would be really grateful as I'm understanding parts of the solution but not whole. Thanks.

In contest, I got Accepted at the problem D, but when the system tested I got TLE on test 8, but in contest it passed :(. The only thing that I changed today was instead of long long I put int and passed. Why that happened?

During the contest, not all test cases are run. You would have got the correct answer for the tests that were run during the contest. After the contest was over, when all test cases are run, there must be some test cases in which your code didn't run in time. Changing long long to int would have solved the problem because computation on integers takes about half as much time as computation on long long integers. This is because in some machines, the size of the CPU register is 32 bits and long long takes 64 bits. I think it is also dependent on the compiler but not sure.

Question F can be solved in O(n^3) without the log factor. And according to my solution, once we got the permutation, we need not check it again whether it satisfies with the input segments. My submission

It can be solved even in $$$O(n^2)$$$ https://mirror.codeforces.com/blog/entry/76306?#comment-608280

vovuh Maybe you want to mention that there is a $$$O(n^2)$$$ solution

https://mirror.codeforces.com/contest/1343/submission/77564353 This is my solution for D which I submitted during contest. It gave me TLE in system testing on TC11. Now i copied exactly the same code and submitted it after the contest(and after the system testing) https://mirror.codeforces.com/contest/1343/submission/77619357. This is the link for the same. It is Accepted by the system. moreover i have submiited the same code 3 -4 times after contest it is showing AC every time. Now can somoene please explain to me why is all this happening and if my code is AC will i get marks for it??

plz organizers revert to this vovuh[user:vovuh]

Can anyone please tell me why I am getting wrong answer on test case 4 in problem E

My Approach :-

Find all the edges on shortest route from a to b using bfs

Find all the edges on shortest route from b to c using bfs

Sort the price array

Assign lowest prices to common edges in path from a to b and b to c

Assign lowest prices among the prices left to remaining edges in routes

Code Link :- https://mirror.codeforces.com/contest/1343/submission/77562702

This algorythm simply does not give the optimal assignment.

You would not have to find the shortest route from b to c, but instead the shortest path from any vertex in path from a to b, to c. But considering that the part from that vertex to b counts twice. So you end up with the turorials solution.

Can you please explain a little more why my method is not giving optimal assignment. Or give any test case on which it does not give optimal solution.

Assume graph, with edges a-x, x-c, x-x1, x1-x2, x2-b, and some path from b to c which is not the one over x, but one element shorter than that path.

With your algo you find cheapest assignment of all nodes in path a-b-c. But assignment for path a-x-b-x-c can be better, depending on p[] values.

Okay! I got it now. I didn't considered the case when there are multiple shortest path from b to c. Thank you very much for taking out time to clear my doubt.

Why aren't editorials posted here?

In 1343A why if I place break statement after if loop it's not working??

in this prblm if we print n itself then it should be correct na ??? because for k = 1 --> x == n always satisfy the solution .

theres nowhere written that x can't be n .

Are you internet explorer.... because you seem to be late.

MikeMirzayanov orz

For E i tried running bfs from a to b and then b to c and marked the used edges in a map and then counted edges having frequency two = repeated_edges and added these many least weighed edges twice and others once from the weight array but it is failing on tc — 4 case 320 can someone please point out the error.

https://mirror.codeforces.com/contest/1343/submission/77633200

use this test case draw on paper and think why it failed. I was facing exactly the same issue.

Thanks for replying but my code is giving correct output for the test case u gave.

vovuh IN problem: (F) Restore the Permutation by Sorted Segments

for last test case

5

2 2 5

3 2 3 5

4 2 3 4 5

5 1 2 3 4 5

why 1 4 3 2 5 is wrong answer (correct as per test case:2 5 3 4 1)

I got it. sorry i bothered you

Could you explain in detail why the permutation is wrong?

you have to choose some r between 2 to n according to that 5 can not occur at last position as it is part of every segment

My approch was to find element with frequency 1 in all segments that could be the last elemnet of our permutaion(if only one element than it is last for sure)

remove that segment keep repating this until we get array of n-2

and I have to check for the order of last 2 remaing elements some how which will be our first and second

but I cound't figure it out

Actually I can not solve the problem independently. So I am so sorry that I can not help you.

min(ai,an−i+1)+1;max(ai,an−i+1)+k , why is the left side not mini(ai,an -i + 1) — 1, why +1

let {a[i],a[n-i+1]} be the pair of elements, then whats the minimum sum of this pair possible by replacing at most 1 of the two elements so the operation cost is 1, so we will take the minimum of the two pair unchanged and will change the maximum of the pair to 1 as the minimum number we can replace to is 1. So it becomes min(a[i], a[n-i+1])+1. Hope it helps.

Could anyone (maybe vovuh) please look my solution of D and help me hack this solution, if its possible!

Idea is very simple: Just try some values of sums (i.e. x) close to K, along with some most frequently occuring sums.

Can you please help me what is wrong in my solution for D (Brute Force), I'd be grateful:

your function counting the changes is incorrect:

eg. K(as per given in problem) = 3, v[i] = {1, 1}, k = 5. Here, changes required are 2(i.e. {1, 1} -> {2, 3}), but your function counts only 1 change.

Yes, figured that out. Can you please tell me the correct conditions for counting changes? Are these correct:

You can refer my solution for the correct conditions.

What is the proof for E, that the optimal path always looks like this :a→x , x→b, b→x and x→c ?

Let the paths $$$a = v_1 ... v_n = b$$$, $$$b = v'_1 ... v'_m = c$$$ be optimal. Choose minimal $$$i$$$ such that $$$v_i \in {v'_1 ... v'_m}$$$, say $$$v_i = v'_j$$$. $$$i <= n$$$ since $$$v_n \in {v'_1 ... v'_m}$$$. Let $$$P_1 = (v_i, ... ,v_n), P_2 = (v'_1 ... v'_j)$$$. Let $$$rev(P)$$$ for path $$$P$$$ be the reverse of that path.

There are cases:

$$$P_1 \not = rev(P_2)$$$. WLOG say the length of $$$P_1 \geq $$$ length of $$$P_2$$$. Then we can replace the $$$ab$$$ path with $$$v_1, v_2 ... v_{i - 1}, rev(P_2)$$$. This new $$$ab$$$ path is not longer then the old $$$ab$$$ path so we can do this.

$$$P_1 = rev(P_2)$$$. Then take $$$x = v_i$$$ and we have paths $$$a \rightarrow x$$$ is $$$v_1 ... v_i$$$, $$$x \rightarrow b$$$ is $$$v_i ... v_n$$$, $$$b \rightarrow x$$$ is $$$v'_1 ... v'_j$$$ and $$$x \rightarrow c$$$ is $$$v'_j ... v'_m$$$.

https://mirror.codeforces.com/contest/1343/submission/77590860 problem D, can anyone tell me an anti-testcase?

(if dist(a,x)+dist(b,x)+dist(c,x)≤m). can anybody please explain this line to me in editorial of problem E?

I post a reply to someone below. Hope you work out the problem after seeing my post. Thanks very much.

can you also tell me some kind of proof that why this a→x , x→b, b→x and x→c path is always optimal, in the editorial it's written that this is it no proof given, if iam missing some points please highlight (vovuh)

Finally reached expert...Thanks for the contest.. Qestion D was really nice ..

problem E:why is the condition

dist(a,x)+dist(b,x)+dist(x,c)≤mnecessary?Because the length of p is m, so the length of the array containing prefix sum of p is m. You may get runtime error if dist(a,x)+dist(b,x)+dist(c,x) is greater than m

How can we be sure that dist(a,x)+dist(b,x)+dist(c,x) is not the answer?

If we can find a smaller dist(a,x')+dist(b,x')+dist(c,x'), the current dist(a,x)+dist(b,x)+dist(c,x) is not the answer. so just for each point update the minimum and print it.

Finally, I know why we should ignore da[x] + db[x] + dc[x] > m case. Because we assume x the first point where path a->b and b->c intersects, which means that path a->x, b->x, c->x don't have common edges. so the sum of their length can't be longger than the total edge number m. If da[x] + db[x] + dc[x] > m, then it cann't be the intersection point we need to find

Thanks! That is right. You get a deeper understanding than me!

I created a test case which hacked the solution in tutorial. Is the std wrong or my test case illegal?

the test case: 1 6 2 1 3 3 1 3 4 2 1 4 2 2 5 2 2 6 The std output nothing. Thanks very much for testing my test case

I was thinking the same about problem E. But I was and still in doubt that How we can assure that path a -> x and x -> c will not have any common edges.

As the tutorial is saying: "like three straight paths with one intersection point x", I am not getting this, How can we assure about three straight paths always?

Could somebody help me with this? Thanks!.

x->c can have edges which are common with x->a or x->b . If it's x->a, then we have 2 cases: 1) x->c has all edges from x->a (path is x->a->c and common edges are the edges from x->a) or 2) there is some point y in between 'a' and 'x' such that the edges from x->y is common (i.e x->y->c, a->y->x and common edges are the edges from y->x). In the first case, if 'x' is not 'a', then having x=a will always give better answer as x->a +x->b + x->c will be smaller and you have a longer prefix x->b. In second case, you can have x=y which will give a smaller answer because of the same reason mentioned above. Similarly, you can work out for edges which are common to x->b. The point is that the algorithm will find surely find the optimal answer (x=a or x=y in above case) if there exists one.

Can someone explain the following code in Problem C — auto sgn = [&](int x) { if (x > 0) return 1; else return -1; }; how auto keyword is used here and materials to read to understand this code. Please!

This is the function that returns the "sign" of an integer. +1 for positive X, -1 for negative. You can google it: https://stackoverflow.com/questions/7951377/what-is-the-type-of-lambda-when-deduced-with-auto-in-c11

I was unaware of lambda functions in c++. Thanks for helping

Detailed Explanation for D

Can somebody please explain why I am getting WA on E Submission Link

Final ab & bc paths not always necessarily shortest paths between a-b or b-c. One of the longer paths could have more vertexes in common thought better weight sum. Plus, Dijkstra has o(n*ln(n)) complexity and should fail on big inputs since, as stated in the editorial, for this problem it is sufficient to make liner 5 passes.

I have actually calculated shortest paths from a-b ,b -c, a-c , if path from len(a-b) = len(a-c) + len(b-c) then c occurs in one of the shortest path from a to b and that path should be considered for optimal soln. otherwise the path from a-b (shortest ) and b-c shortest is considered .Though due to TL the soln might get TLEd but I want to know If the above approach is incorrect!! :)

BTW, Thanks for the reply !!

Yep, it is incorrect. Shortest a-b path does not always appear in the best possible solution. If you have p[weights] = {1,..(9 ones)..,1,100,100,100...} and graph: 1-(5edges)-6-(5edges)-11, and from vertex 6-(6edges)-x=a,c (x connected to both a and c by 1 edge each), then a,b,c = 1, 6, 7. Shortest paths a-b and b-c are 5 vertexes each. But since you have only 9 ones, your result with the shortest paths would be 109. But if you'll go through point x, your result ould be 1+6*2+1 = 14. Or through the point a with result 12.

Or imagine rhombus with vertexes a,b,c,x. With 10 edges between a and b, 10 between b and c, and with 6 edged between each pair: a-x, b-x, c-x. If you have only 19 ones and a lot of hundreds among edge weights, your cheapest path would lay through point x, and it has no common edge with either of shortest paths a-b or b-c.

Nice editorial! I really enjoyed the problems.

Here is a submission for problem F with comments. I think it's clear and easy to understand . But if there are questions feel free to ask. https://mirror.codeforces.com/contest/1343/submission/77673993

HI I have a question related to Problem A:

geometric sequence tells that = 2^(k-1)

but in the tutorial you said: ((2^k)-1)

anyone please explain???

well 2^0 + 2^1 + ... + 2^(k-1) = (2^k)-1

How Problem D can be solved using Binary search?

I built a vector that holds the minimum value every pair can take with one change, and a vector that holds the maximum value every pair can take with one change. Fix a target $$$1 <= x <= 2k$$$ that you want every pair to equal after your changes. The number of pairs whose min is > x will require 2 changes, as will the number of pairs whose max is < x. You can binary search for the number of pairs that fulfill these conditions, using something like lower_bound(mins.begin(), mins.end(), x). You can also see that a pair cannot fulfill both of these conditions simultaneously, so we don't double count.

auto sgn = [&](int x) { if (x > 0) return 1; else return -1; }; what does this code do ?

If x is positive return 1,else if x is negative return -1. You can read more about it here.

In problem F the permutation is not necessarily unique! In general, if all given intervals are of length 2 the permutation can be reversed and still be correct. Those should be the only 2 possible permutations

One can also reconstruct the array from the last element to the first: The last element can only occur in one segment and there can be at most two elements which occur only once (the last and maybe the first). So if there is only one element it has to be the last. If there are two we can just test both but fixate the other one as the first element. If the first element is fixed we will only find one other element which occurs only once at every moment so we will find at most two permutations (those are the only two possible permutations). We can check both for correctness and print the right one.

My Implementation: 77696766

I said that the permutation can be uniquely restored if the first element is fixed. Reread the editorial please. I didn't say that there is only one possible answer.

Thanks for the clarification, though I don't get why someone would downvote MZienni. This sentence: "One interesting fact: if

suchpermutation exists then it can be restored uniquely." really bear some ambiguity.For problem, 1343E — Weights Distributing, am getting wrong answer on test 3, Error says: 35th numbers differ — expected: '4', found: '3' Any idea why? Not able to get the failing test case as it was too long My solution link

This initialization of

`ans=cost[-1]+1`

, what does it do? In C++ we would need to initialize it with`ans=1e18`

Thanks for spotting the issue. I took the last index of prefix sum array and added one assuming that would be the max possible value, but did not consider the fact that there were 2 prefix sum additions in the answer. Did submit a fix, and it passed the 3rd test case, but got a TLE at 19th TC. Thank you !

why difficulty of problem F is 2800? lol, it is strange, who set difficulties?

what is the significance of this statement "It is guaranteed that the sum of n over all test cases does not exceed 2⋅105 (∑n≤2⋅105)"

Since all testcases must be finished within the timebox of one second it is important to know how much data must be processed. Without that statement the sum of n over all test cases could be up to 1e5 * 1e4 == 1e9 which is significantly different.

thank you @spookywooky : )

What's wrong with B problem editorial explaination?

In Editoral vovuh wrote that->(This array is almost good except one thing: the sum in the right half is exactly less than the sum in the left half. So we can fix it easily: just add n/2 to the last element.)

But in tutorial code this line is look like ->

(cout << 3 * n — 1 << endl;)

How (3*n — 1 == n/2)?

For the other elements the output is

`cout << i * 2 - 1 << " ";`

So, adding n/2 for the case that i==n/2 we get

`cout << 3 * n - 1 << endl`

Note that n is devided by two earlier.

Thank You very much..

Hello, in problem C, vovuh has something called sgn, is that a function or something else? Could someone explain it or what it is called so I could find a tutorial?

Thanks in advance

It's short for sign: +1 or -1. And code is there too:

auto sgn = [&](int x) { if (x > 0) return 1; else return -1;

Thanks for the reply, I have seen the code, but I have never seen this syntax, by this I mean [&] being in front of (int x), because this does not seem like a function.

You can just search the internet for it: [=] vs [&]

1343E - Weights Distributing Can anyone help me in my code it says wrong ans for test 4 https://mirror.codeforces.com/contest/1343/submission/77737942

Final ab & bc paths not always necessarily shortest paths between a-b or b-c. One of the longer paths could have more vertexes in common thought better weight sum.

thanks man

https://mirror.codeforces.com/blog/entry/76352?#comment-609399

For problem E, why can we ignore dist(a,x)+dist(b,x)+dist(c,x)>m case? Don't say array index out of range, we can use other methods compute this

What do you mean? We can't ignore it: a, b, c (and x) can all be even the same point. And 0 <= m is the solution.

oh, some typo. I mean dist(a,x)+dist(b,x)+dist(c,x)>m case

We can't ignore it either: for graph 1-2-3-4-5 (m = 4) in case a=c=1, b = 5 the answer is sum(dist()) = 2*m > m.

but in the sample code:

Oh, this means that point x is too far from a,b,c to be solution and pref[da[i] + db[i] + dc[i]] index would be out of range.

Finally, I know why we should ignore da[x] + db[x] + dc[x] > m case. Because we assume x the first point where path a->b and b->c intersects, which means that path a->x, b->x, c->x don't have common edges. so the sum of their length can't be longger than the total edge number m. If da[x] + db[x] + dc[x] > m, then it cann't be the intersection point we need to find

Did anybody solve

Dusing Segment Tree, is it possible?.UPDFoundI tried to solve D using Segment Tree, but got tle on 2nd test case.

Well， I found out why I got TLE. At first I used memset function instead of build_tree to init seg tree. The array is very large(4e5 * 4) so it took too much time to init.

Can someone tell me about assert function more deeply? this function is being used by editorial solution maker??

In c++ assert is a function-like macro. It is used for early error detection: if assert() fails — there some logical mistakes or misspell.

why do we need this function ? I mean if we write our code wrong the compiler would tell us about it cleary so why this function is here?

https://mirror.codeforces.com/blog/entry/17199 See the comments.

How to solve problem A?

I didn't understand the tutorial of F. Any help would be appreciated.

First number in permutation would always be in 1 and only 1 segment of size 2. Grab all elements from 2-sized segments and check if there can be formed permutation if it would be the first element: first, exclude it from every segment where you find it — after this, there must be only 1 segment with size "1". This will be the second number. Take this number and exclude it from every segment, now there must be only one segment of size 1. This will be the third number... and so on. When found sequence — check it. If it's good — output, else search next number to be first.

anyone did problem D ? with binary_search approach?..please help

Why

prefmeans at most 1 replacement instead of exactly 1 replacement in Problem D?I've tried to understand it for three days.

Because when we increment one in the segment: [min(a_i, a_{n-i+1}) +1, max(a_i, a_{n-i+1})+k )

We are also incrementing the position a_i + a_{n-i+1} and the x made by a_i + a_{n-i+1} we already have for free.

Can anyone give me the python code to make the prefix array for problem D?

You should really google it — it's a basic concept — it's basically a string of simple code.

Why Problem E can't be solve with two bfs? one bfs from a to other nodes and other bfs from c to other nodes and then I can simulate the junction point of a and c with this two distance, but it is showig WA

In the Problem E, it says:"There are no

loopsor multiple edges in the given graph". Does the "loops" here actually mean "self loops"? In my opinion, the second example contains "loops". Am I wrong ?Yes, the meaning is "There are no self loops or...". Of course, there are loops in the graph.

Easy implementation of F

78569543

What's the 373th TestCase of Test 2 ?

Wouldn't the complexity of solution provided for F be O(n^4*logn) as comparing sets take linear time? MikeMirzayanov

Can someone explain what is meant by "the parities of halves won't match" in tutorial of problem B?

The sum of numbers in the first half is even, since all values are even. If the size of the half array is odd, then the sum of the second half will be odd, too. Since the sum of the halfes must be same this leads to no solution possible.

In Alternating Subsequence problem, one test case is [-2 8 3 8 -4 -15 5 -2 -3 1]. The longest alternating subsequence is [-15 5 -2]. Hence the answer should be -12. But given solution is [-2 8] => 6. Please help me with this.

D can also be solved using policy based DS. https://mirror.codeforces.com/contest/1343/submission/97821782

n &1 what do you mean by this ??

See this first. So,

n&1 denotes the parity(odd/even) of the number. If number is odd n&1 equals 1 and for even 0.

Problem E is so good

A is too hard than B, unfair

Why we do j-1 in problem C? Can somebody explain?